WASHINGTON — The Obama administration, resolving years of internal debate, is on the verge of backing a Federal Bureau of Investigation plan for a sweeping overhaul of surveillance laws that would make it easier to wiretap people who communicate using the Internet rather than by traditional phone services, according to officials familiar with the deliberations.

The F.B.I. director, Robert S. Mueller III, has argued that the bureau’s ability to carry out court-approved eavesdropping on suspects is “going dark” as communications technology evolves, and since 2010 has pushed for a legal mandate requiring companies like Facebook and Google to build into their instant-messaging and other such systems a capacity to comply with wiretap orders. That proposal, however, bogged down amid concerns by other agencies, like the Commerce Department, about quashing Silicon Valley innovation.